Vol. 301, No. 1, 2019

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Multiplicity upon restriction to the derived subgroup

Jeffrey D. Adler and Dipendra Prasad

Vol. 301 (2019), No. 1, 1–14
DOI: 10.2140/pjm.2019.301.1
Abstract

We present a conjecture on multiplicity of irreducible representations of a subgroup H contained in the irreducible representations of a group G, with G and H having the same derived groups. We point out some consequences of the conjecture, and verification of some of the consequences. We give an explicit example of multiplicity 2 upon restriction, as well as certain theorems in the context of classical groups where the multiplicity is 1.

Keywords
reductive group, derived subgroup, representation, restriction, multiplicity
Mathematical Subject Classification 2010
Primary: 22E50
Milestones
Received: 10 June 2018
Accepted: 5 September 2018
Published: 16 September 2019
Authors
Jeffrey D. Adler
Department of Mathematics and Statistics
American University
Washington, DC
United States
Dipendra Prasad
Indian Institute of Technology
Mumbai
India
Tata Institute of Fundamental Research
Mumbai
India
Laboratory of Modern Algebra and Applications
Saint-Petersburg State University
Russia